we can say that if the cost per meter of laying pipes along the rural roads is less than the cost per meter of laying pipes through the field, then it would be less expensive to lay the pipes along the rural roads.
What is meter?
A meter is a unit of length in the International System of Units (SI). It is defined as the length of the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second. The symbol for meter is "m".
To determine which option is less expensive, we need to compare the cost of laying pipes along the rural roads to the cost of laying pipes through the field.
Let's assume that we need to lay a water pipe that is 100 meters long. If we choose to lay the pipe along the rural roads, the cost would be:
Cost = length of pipe x cost per meter = 100 x $3.00 = $300.00
If we choose to lay the pipe through the field, the cost would be:
Cost = length of pipe x cost per meter = 100 x $4.50 = $450.00
Therefore, laying the pipe along the rural roads would be less expensive in this case, with a cost of $300.00 compared to $450.00 for laying the pipe through the field.
In general, we can say that if the cost per meter of laying pipes along the rural roads is less than the cost per meter of laying pipes through the field, then it would be less expensive to lay the pipes along the rural roads. Conversely, if the cost per meter of laying pipes through the field is less than the cost per meter of laying pipes along the rural roads, then it would be less expensive to lay the pipes through the field.
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Full question:
It costs $3.00 per meter for the water pipes to go along the rural roads and $4.50 per meter for the water pipes to go through the field. Which option is less expensive? Explain how you found your answer.
Design a box that will hold 24 2-in cubes, with no empty space left in the box after it is filled with the cubes. Describe two possible designs for the box. Sketch each design and find the surface area and volume of each box.
Below given are two possible designs for the box.
The total surface area is 2(12) + 2(8) + 2(10) = 24 + 16 + 20 = 52 square inches.
What is total surface area?Total surface area is the sum of the areas of all the faces of a three-dimensional object.
Design 1:
One possible design for the box is a rectangular prism with dimensions of 4 in x 4 in x 6 in. This box will have enough space to hold 24 2-in cubes with no empty space left in the box after it is filled with the cubes.
To find the surface area and volume of the box, we can use the following formulas:
Surface Area = 2lw + 2lh + 2wh
Volume = lwh
where l, w, and h represent the length, width, and height of the box, respectively.
In this case, we have:
l = 4 in
w = 4 in
h = 6 in
So the surface area of the box is:
Surface Area = 2(4)(4) + 2(4)(6) + 2(4)(6)
Surface Area = 112 in²
And the volume of the box is:
Volume = 4(4)(6)
Volume = 96 in³
Design 2:
Another possible design for the box is a cube with dimensions of 3.4 in x 3.4 in x 3.4 in. This box will also have enough space to hold 24 2-in cubes with no empty space left in the box after it is filled with the cubes.
To find the surface area and volume of the box, we can use the same formulas as before, but with the new dimensions:
l = 3.4 in
w = 3.4 in
h = 3.4 in
So the surface area of the box is:
Surface Area = 2(3.4)(3.4) + 2(3.4)(3.4) + 2(3.4)(3.4)
Surface Area = 69.12 in²
And the volume of the box is:
Volume = 3.4(3.4)(3.4)
Volume = 39.3 in³
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HELP ASAP
A composite figure is represented in the image.
A four-sided shape with the base side labeled as 21.3 yards. The height is labeled 12.8 yards. A portion of the top from the perpendicular side to a right vertex is labeled 6.4 yards. A portion of the top from the perpendicular side to a left vertex is labeled 14.9 yards.
What is the total area of the figure?
272.64 yd2
231.68 yd2
190.72 yd2
136.32 yd2
the total area of the figure is 412.16 yd² and closest option is 272.64 yd²,.
To find the area of a composite figure, we need to break it down into simpler shapes and add up their individual areas. In this case, we can divide the figure into a rectangle and two right triangles.
First, let's calculate the area of the rectangle. The base of the rectangle is 21.3 yards and the height is 12.8 yards. Therefore, the area of the rectangle is:
Area of rectangle = base x height
= 21.3 yd x 12.8 yd
= 272.64 yd²
Next, let's calculate the area of the right triangles. We can find the height of each triangle using the Pythagorean theorem.
For the triangle on the right side, we know the base is 6.4 yards and the hypotenuse is 21.3 yards (the same as the base of the rectangle). We can solve for the height (h) using the Pythagorean theorem:
h² + 6.4² = 21.3²
h² = 21.3² - 6.4²
h² = 410.45
h = √410.45
h ≈ 20.26 yards
The area of this triangle is:
Area of right triangle = (1/2) x base x height
= (1/2) x 6.4 yd x 20.26 yd
= 64.96 yd²
For the triangle on the left side, we know the base is 14.9 yards and the hypotenuse is also 21.3 yards. We can solve for the height (h) using the Pythagorean theorem:
h² + 14.9² = 21.3²
h² = 21.3² - 14.9²
h² = 99.94
h = √99.94
h ≈ 9.997 yards (rounded to three decimal places)
The area of this triangle is:
Area of left triangle = (1/2) x base x height
= (1/2) x 14.9 yd x 9.997 yd
= 74.56 yd²
Now, we can find the total area of the figure by adding up the areas of the rectangle and the two triangles:
Total area = area of rectangle + area of right triangle + area of left triangle
= 272.64 yd² + 64.96 yd² + 74.56 yd²
= 412.16 yd²
Therefore, the total area of the figure is 412.16 yd².
However, none of the given answer choices match this result. The closest option is 272.64 yd², which is the area of the rectangle only. This suggests that there may be an error in the problem statement or answer choices. If we assume that the area of the figure is intended to be the area of the rectangle only, then the answer is indeed 272.64 yd².
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please help!!!!!!!!!
Answer:
$7734.82
Step-by-step explanation:
You want to know the amount that will result in $20,000 after 20 years when 4.75% interest is compounded continuously.
Continuous compoundingThe formula for account value is ...
A = P·e^(rt)
We want to find P when A=20,000, r=0.0475, and t=20.
20000 = P·e^(0.0475·20)
P = 20000·e^(-0.0475·20) ≈ 7734.82
You would have to deposit $7734.82 in the account to have $20,000 in 20 years.
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1
Which expression has a value of 36?
Answer: (1/6)^2
Step-by-step explanation:
Answer:
The third answer is correct
Step-by-step explanation:
Use the properties of degrees:
1)
[tex] {( \frac{1}{108} })^{3} = \frac{ {1}^{3} }{ {108}^{3} } = \frac{1}{6561} [/tex]
[tex] \frac{1}{6561} ≠ \frac{1}{36} [/tex]
.
2)
[tex] ({ \frac{1}{9} })^{3} = \frac{ {1}^{3} }{ {9}^{3} } = \frac{1}{729} [/tex]
[tex] \frac{1}{729} ≠ \frac{1}{36} [/tex]
.
3)
[tex] ({ \frac{1}{6} })^{2} = \frac{ {1}^{2} }{ {6}^{2} } = \frac{1}{36} [/tex]
[tex] \frac{1}{36} = \frac{1}{36} [/tex]
The aquarium has 1 fewer red fish than blue fish. 60% of the fish are blue. How many blue fish are in the aquarium? Show your work.
Write as text so i can paste please
Answer:
3
Step-by-step explanation:
If blue, then 60%. 2/5 are red and 1/3 are blue. Two redfish and three bluefish are present. if the aquarium has 1 fewer redfish than bluefish. 60% of the fish are blue. There are 5 out of 3 blue fish in the aquarium.
PLEASE HELP!!!!! MIDDLE SCHOOL MATH!!!!!!!!!!!!
Use the figure shown. Match each angle to the correct angle measure. Some angle measures may be used more than once or not at all.
PLEASE LOOK AT THE PICTURE BELOW!!!!! SHOW WORK!!!!!!!!
The measures of the angles are:
m ∠GAL = 90°
m ∠LAO = 71°
m ∠CAO = 109°
m ∠KAC = 71°
Determining the measures of anglesFrom the question, we are to determine the measure of the angles
m ∠GAL = 90° (Right angle)
m ∠LAO
m ∠LAO + m ∠GAL + 19° = 180° (Sum of angles on a straight line)
m ∠LAO + 90° + 19° = 180°
m ∠LAO = 180° - 90° - 19°
m ∠LAO = 90° - 19°
m ∠LAO = 71°
m ∠CAO
m ∠CAO = m ∠KAL (Vertically opposite angles)
m ∠KAL = m ∠GAL + 19°
m ∠KAL = 90° + 19°
m ∠KAL = 109°
Therefore,
m ∠CAO = 109°
m ∠KAC = m ∠LAO (Vertically opposite angles)
m ∠LAO = 71°
Therefore,
m ∠KAC = 71°
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A grain silo has a cylindrical shape. Its radius is 9 ft, and its height is 49 ft. What is the volume of the silo?
Use the value 3.14 for , and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Check
9 ft
49 ft
0
ft
X
ft²
Therefore, A grain silo has a cylindrical shape the answer is: 12,689 ft³ (cubic feet).
What is percentage?Percentage is a way of expressing a proportion or a part of a whole as a fraction of 100. It is represented by the symbol % (per cent), which means "per hundred". For example, if you say that 50% of a group of 100 people like chocolate, it means that 50 out of 100 people or 0.5 (50/100) of the total group like chocolate. Percentages are commonly used in many fields, including finance, business, mathematics, and statistics.
The formula for the volume of a cylinder is:
V = π[tex]r^{2}[/tex]h
where V is the volume, r is the radius, and h is the height.
Substituting the given values, we get:
[tex]V = 3.14 *9^2 *49[/tex]
[tex]V = 12,689.46[/tex]
Rounding to the nearest whole number, the volume of the silo is approximately 12,689 cubic feet.
Therefore, the answer is:
12,689 ft³ (cubic feet)
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Simplify this expression:
X^3y^-2x/x^-3y^8
HELP.
solve for w
w+2/5=3 1/3
The fractions as 50/15 and 6/15, respectively, and subtract them to obtain w = 44/15. This can be further simplified to the mixed number 2 14/15 or the decimal approximation 2.933.
To solve the equation w + 2/5 = 3 1/3, we need to isolate w on one side of the equation by subtracting 2/5 from both sides, finding a common denominator, and simplifying the resulting expression to obtain w.
w + 2/5 = 10/3
To isolate w, we need to move the constant term on the right-hand side of the equation to the left-hand side by subtracting 2/5 from both sides.
Subtracting 2/5 from both sides:
w = 10/3 - 2/5
To add these fractions, we need to find a common denominator, which is 15. So we can rewrite the fractions as:
w = (50/15) - (6/15)
Combining like terms:
w = 44/15
Therefore, w = 2 14/15 or approximately 2.933.
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Gopal, Krishna and Govind are partners sharing profits and losses in the ratio of 5 4 3. Krishna retired on 1st April, 2022. Gopal and Govind purchased her share of profit by giving her 1,20,000, 80,000 being paid by Gopal and 40,000 by Govind. The gaining ratio will be: (a) 5:3 (b) 4:3 (c) 1:1 (d) 2:1
If Gopal, Krishna and Govind are partners sharing profits and losses in the ratio of 5 4 3. The gaining ratio will be: (a) 5:3.
How to find the gaining ratio?Since Krishna is retiring, her share of profit will now be divided between Gopal and Govind in the same ratio as their existing profit-sharing ratio.
The total amount paid to Krishna is 1,20,000. Out of this, Gopal has paid 80,000 and Govind has paid 40,000.
So, the share of profit purchased by Gopal is:
5/12 x 120,000 = 50,000
And the share of profit purchased by Govind is:
3/12 x 120,000 = 30,000
Now, the total profit sharing ratio of the remaining partners (Gopal and Govind) will be:
5:3 + 3:3 = 8:3
Therefore, the gaining ratio will be:
Gopal = 50,000 / (50,000 + 30,000) = 5/8
Govind = 30,000 / (50,000 + 30,000) = 3/8
So, the gaining ratio of Gopal and Govind will be 5:3, which is option (a).
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What is the answer for radius and diameter?
Answer:
11 and 22
Step-by-step explanation:
radius is
r = 11 cm
diameter is
d = 2r = 2×11 = 22cm
NEED BY 20 mins !!!! You synthetic division to determine whether the first expression is a factor of the second if it is indicate it
Answer:
Step-by-step explanation:
32
An investor considers investing $10,000 in the stock market. He belives that the probability is 0.30 that the economy will improve, 0.40 that it will stay the same, and 0.30 that it will deteriorate. Further, if the economy improves, he expects his investment to grow to $15,000, but it can also go down to $8,000 if the economy deteriorates. If the economy stays the same, his investment will stay at $10,000. What is the expected value of his investment?
Using Expression for Investment, the expected value of the investor's investment is $10,900.
What exactly are expressions?
In mathematics, an expression is a combination of numbers, symbols, and operators that can be evaluated to produce a value. An expression can represent a number, a variable, or a more complex combination of mathematical objects.
Now,
The expected value of the investor's investment can be calculated as follows:
E(investment) = E(investment | economy improves) * P(economy improves) + E(investment | economy stays the same) * P(economy stays the same) + E(investment | economy deteriorates) * P(economy deteriorates)
where E(investment | economy improves), E(investment | economy stays the same), and E(investment | economy deteriorates) are the expected values of the investor's investment under each scenario.
If the economy improves, the investor's investment is expected to grow to $15,000, so:
E(investment | economy improves) = $15,000
If the economy stays the same, the investor's investment will stay at $10,000, so:
E(investment | economy stays the same) = $10,000
If the economy deteriorates, the investor's investment is expected to go down to $8,000, so:
E(investment | economy deteriorates) = $8,000
Putting it all together, we get:
E(investment) = $15,000 * 0.30 + $10,000 * 0.40 + $8,000 * 0.30
E(investment) = $4,500 + $4,000 + $2,400
E(investment) = $10,900
Therefore, the expected value of the investor's investment is $10,900.
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A regular is 7 -sided figure heptagon whose sides all have equal length. Find the perimeter of a regular that has a side of 12.75 inches. Question content area bottom Part 1 The perimeter of the regular is enter your response here ▼ square inches. cubic inches. inches. (Simplify your answer. Type an integer or a decimal.)
Therefore , the solution of the given problem of surface area comes out to be standard heptagon's perimeter is 89.25 inches as a result.
What does an area actually mean?By calculating how much space would be needed to fully enclose its exterior, its overall size can be calculated. The surrounding region is considered when selecting a comparable product in the rectangular design. The surface area of something determines its overall dimensions. The number of sides connecting a cuboid's four trapezoidal forms determines how much water it can hold.
Here,
By dividing the length of one side by the heptagon's total number of sides, which is seven, one can determine the perimeter of a standard heptagon with sides measuring 12.75 inches in length.
The circumference P is thus:
=> P = 7(12.75)
=> 89.25 inches at P.
The standard heptagon's perimeter is 89.25 inches as a result.
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In a sample of 100 planters mixed nuts 13 were found to be almonds.
A)construct a 99 percent confidence interval for the true proportion of almonds
B)May normality be assumed
C) what sample size would be needed for 99 percent confidence and an error of 0.05
ANSWER ALL URGENT
or Part A, we can use the formula for confidence intervals:
CI = p ± Zsqrt((pq)/n)
where p is the proportion of almonds found in the sample (13/100 = 0.13), q is 1-p, Z is the z-value for a 99% confidence level (2.576), and n is the sample size (100). Plugging in these values, we get:
CI = 0.13 ± 2.576sqrt((0.130.87)/100)
which simplifies to:
CI = (0.045, 0.215)
Therefore, we are 99% confident that the true proportion of almonds in the population of planters mixed nuts is between 0.045 and 0.215.
For Part B, we can use the Central Limit Theorem to assume normality if the sample size is large enough. Since n = 100 is greater than or equal to 30, we can assume normality.
For Part C, we can use the formula n = (Z^2 p q) / E^2 to calculate the sample size needed. Here, Z is the z-value for a 99% confidence level (2.576), p is the estimated proportion of almonds (0.13), q is 1-p, and E is the maximum error of the estimate in decimal form (0.05). Plugging in these values, we get:
n = (2.576^2 0.13 0.87) / 0.05^2
which simplifies to approximately 276. Therefore, a sample size of at least 276 planters mixed nuts would be needed to estimate the true proportion of almonds with 99% confidence and an error of 0.05
A box contains ten balls , numbered 1 through 10. Marisha draws a ball. She records its number and then returns it to the bag. Then Penney draws a ball. Fine each probability.
P(9,then 3)
Answer:
1.P(9,then 3) = (1/10)*(1/10)=1/100
Step-by-step explanation:
hope it helps and no explanation
Amadou and Olivia are making fruit salads for a picnic. Amadou mixes 9 cups of melon and 10 cups of apple and Olivia mixes 2 cups of melon and 3 cups of apple. Use Amadou and Olivia’s percent of apple to determine whose fruit salad will taste more appley.
Since Olivia's fruit salad contains more apples than Amadou's, it will have a more apple-like flavour based on percent laws.
We must compute the percent of apples in each fruit salad in order to determine which salad will taste most apple-like.
Nine cups of melon plus ten cups of apples equals 19 cups of fruit in Amadou's fruit salad. Therefore, the fruit salad Amadou made contains:
10 cups of apples divided by 19 cups of fruit equals 100% of the percentage of apples in Amadou's fruit salad, or 52.63%.
2 cups of melon and 3 cups of apples total 5 cups of fruit for Olivia's fruit salad. So, there are: in Olivia's fruit salad.
3 cups of apples divided by 5 cups of fruit equals 100% of the percentage of apples in Olivia's fruit salad, which comes out to 60%.
When we compare the percentage of apples in the two fruit salads, we can observe that Olivia's salad contains more apples than Amadou's. Olivia's fruit salad will therefore taste more apple-like.
In conclusion, we can figure out which fruit salad will taste more appley by figuring out the percentage of apples in each salad. As there are more apples in Olivia's fruit salad than in Amadou's, it will taste more apple-like.
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ASAP ASAP SOMEONE PLEASE HELP, I know its a lot, but someone solve please
ASAP stands for "as soon as possible". It is often used when something needs to be done quickly or urgently. When someone says "ASAP someone please help", it means that they need help immediately and cannot wait any longer.
If you find yourself in this situation, the first step is to identify the problem and determine what needs to be done. Once you have a clear understanding of the situation, you can then reach out to someone who can help you. It's important to be specific when asking for help. Provide as much information as possible so that the person you are asking can understand the situation and offer the best possible assistance.
In summary, there is no shame in asking for help. It's better to reach out for assistance when you need it rather than struggle on your own. Don't hesitate to ask for help when you need it, and always be grateful to those who offer their assistance.
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Which equation represents this statement?
The product of 1/5 and a number is equal to 1 1/2.
Responses
PLS HELP ASAP
Answer:
The answer to your problem is,
[tex]\frac{1}{5} n = l\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{1}{5} * n = l \frac{1}{2}[/tex]
[tex]\frac{1}{5} n = l\frac{1}{2}[/tex]
Thus the answer to your problem is, [tex]\frac{1}{5} n = l\frac{1}{2}[/tex]
There is nothing more to show. But I have picture I did it:
the value of y varies directly as the cube of x and y=20 when x=2. What is y when x=4?
As given the value of y varies directly from the cube of x so after solving the equation and finding the constant of proportionality:
when x=4, y is equal to 160.
What is the constant of proportionality mean?The constant of proportionality is a value that relates two variables that are directly proportional to each other. In a mathematical equation where one variable is directly proportional to another, the constant of proportionality represents the ratio between the two variables.
According to the given informationIf the value of y varies directly from the cube of x, then we can write:
y = kx^3
where k is a constant of proportionality. To find the value of k, we can use the given information that y=20 when x=2:
20 = k(2^3)
20 = 8k
k = 20/8
k = 2.5
Now that we have the value of k, we can use the equation to find y when x=4:
y = 2.5(4^3)
y = 2.5(64)
y = 160
Therefore, when x=4, y is equal to 160.
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Inspection of a random sample of 19 aircraft showed that 15 needed repairs to fix a wiring problem that might compromise safety
A)how large a sample would be needed to estimate the true proportion of jets with the wiring problem with 90 percent confidence and an error of 6 percent
B would the airline actually conduct further sampling or just inspect all the planes
Answer BOTH A and B
or Part A, we can use the formula n = (Z^2 p q) / E^2 to calculate the sample size needed. Here, Z is the z-value for a 90% confidence level, which is 1.645, p is the estimated proportion of jets with the wiring problem (15/19 = 0.7895), q is 1-p, and E is the maximum error of the estimate in decimal form (0.06). Plugging in these values, we get n = (1.645^2 0.7895 0.2105) / 0.06^2, which is approximately 138. Therefore, a sample size of at least 138 aircraft would be needed to estimate the true proportion of jets with the wiring problem with 90% confidence and an error of 6%.
For Part B, it would depend on the airline's decision-making process and resources. Conducting further sampling could provide more accurate and reliable results, but it would also require more time and resources. Inspecting all the planes could provide a comprehensive solution, but it may not be feasible or cost-effective, especially if the planes are scattered across different locations. Ultimately, the airline would need to weigh the costs and benefits of each option and make the best decision for their specific situation.
What is -7(x+6)+12 if x=7
Answer:
-79
Step-by-step explanation:
-7(x+6) + 12 x = 7
-7( 7 + 6) + 12
-7(13) + 12
-91 + 12
-79
So, the answer is -79
Consider a home mortgage of $ 250,000 at a fixed APR of 3 % for 15 years. Complete parts (a) through (c) below. Question content area bottom Part 1 a. Calculate the monthly payment. The monthly payment is $ enter your response here. (Do not round until the final answer. Then round to the nearest cent as needed.
The monthly payment for this mortgage is $1,757.26.
How to calculate the monthly paymentThe following can be deduced from the information:
P = $250,000
r = 0.03/12 = 0.0025
It should be noted that since APR is an annual rate, we need to divide it by 12 to get the monthly rate.
n = 15 × 12 = 180
Since the mortgage is for 15 years and there are 12 months in a year
Monthly payment will be:
= 250000 × (0.0025 × (1 + 0.0025)^180) / ((1 + 0.0025)^180 - 1)
= $1,757.26
Therefore, the monthly payment for this mortgage is $1,757.26.
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5. Let F: V→ W and G: W→ U be isomorphisms of vector spaces over K. Show that GF: V→U is an isomorphism.
GF preserves the identity and addition operations, and hence GF: V→U is an isomorphism.
First, we will show that GF is linear. Let u, v be vectors in V and c be a scalar in K. Then we have:
[tex]GF(cu + v) = G(F(cu + v)) = G(cF(u) + F(v)) = G(cF(u)) + G(F(v))= cG(F(u)) + G(F(v)) = c(GF(u)) + GF(v)[/tex]
Thus, GF is linear.
Next, we will show that GF is bijective. Since F and G are isomorphisms, they are both invertible. Let[tex]F^-1[/tex]and [tex]G^-1[/tex] denote their respective inverses. Then for any u in U, we have:
[tex](GF)^-1(u) = F^-1(G^-1(u))[/tex]
This shows that GF is invertible, and hence bijective.
Finally, we will show that GF preserves the identity and addition operations. Let v1, v2 be vectors in V. Then we have:
[tex]GF(v1 + v2) = G(F(v1 + v2)) = G(F(v1) + F(v2)) = G(F(v1)) + G(F(v2))= GF(v1) + GF(v2)[/tex]
Also, since F and G are isomorphisms, they preserve the identity operations:
[tex]GF(0v) = G(F(0v)) = G(0w) = 0u\\GF(v) = G(F(v)) = G(0w) = 0u if v=0v[/tex]
Thus, GF preserves the identity and addition operations, and hence GF: V→U is an isomorphism.
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how do i calculate an expression in standard or vertex form for this?
According to the given Equation is 1 = 25a + 5b + c.
What is standard vertex?
Standard fοrm and vertex fοrm are twο different ways οf writing the equatiοn οf a quadratic functiοn, which is a functiοn that can be represented by a parabοla.
The standard fοrm οf a quadratic equatiοn is written as:
[tex]y = ax^2 + bx + c[/tex]
where a, b, and c are cοnstants. This fοrm is useful fοr finding the x-intercepts (where the parabοla crοsses the x-axis) οr y-intercept (where the parabοla crοsses the y-axis) οf the graph, as well as the axis οf symmetry.
The vertex fοrm οf a quadratic equatiοn is written as:
[tex]y = a(x - h)^2 + k[/tex]
where a, h, and k are cοnstants. This fοrm is useful fοr finding the vertex (the highest οr lοwest pοint οn the parabοla), as well as the axis οf symmetry.
Bοth fοrms are equivalent, and yοu can cοnvert between them using algebraic techniques. The chοice οf which fοrm tο use depends οn the prοblem yοu are trying tο sοlve and what infοrmatiοn yοu need frοm the equatiοn.
Tο find the standard οr vertex fοrm οf an equatiοn, we need tο use the given pοints tο determine the equatiοn οf a parabοla that passes thrοugh them. A parabοla can be expressed in standard fοrm as:
[tex]y = a x^2 + bx + c[/tex]
οr in vertex fοrm as:
[tex]y = a(x - h)^2 + k[/tex]
where (h,k) represents the vertex οf the parabοla. Tο find the equatiοn οf the parabοla that passes thrοugh the given pοints, we need tο first find the values οf a, b, c οr a, h, k.
Here are the steps tο find the standard fοrm οf the equatiοn:
Write οut the equatiοn in standard fοrm: [tex]y = ax^2 + bx + c[/tex]
Plug in the values οf the pοints intο the equatiοn tο get a system οf equatiοns:
0 = c
1 = 25a + 5b + c
2 = 125a + 25b + c
1 = 9a + 3b + c
0 = 30.25a + 5.5b + c
0 = 36a + 6b + c
Sοlve the system οf equatiοns tο find the values οf a, b, and c. One way tο dο this is tο use matrix algebra οr eliminatiοn/substitutiοn methοd.
Once yοu have the values οf a, b, and c, plug them back intο the standard fοrm equatiοn.
Here are the steps tο find the vertex fοrm οf the equatiοn:
Write οut the equatiοn in vertex fοrm: [tex]y = a(x - h)^2 + k[/tex]
Find the x-cοοrdinate οf the vertex by using the fοrmula: h = -b/2a
Substitute the x-cοοrdinate οf the vertex intο οne οf the οriginal pοints tο find the y-cοοrdinate οf the vertex.
Plug in the values οf the vertex and anοther pοint intο the vertex fοrm equatiοn tο get a system οf equatiοns:
[tex]0 = a(0 - h)^2 + k[/tex]
[tex]2 = a(5 - h)^2 + k[/tex]
Sοlve the system οf equatiοns tο find the values οf a, h, and k.
Once yοu have the values οf a, h, and k, plug them back intο the vertex fοrm equatiοn.
Nοte that the twο fοrms οf the equatiοn will yield the same parabοla, but the vertex fοrm may be easier tο use if yοu need tο find the vertex οr axis οf symmetry.
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Find X
Give step by step explanation please.
Answer:
x = 29
Step-by-step explanation:
The whole circle is 360°.
Theorem regarding angles inside a circle says that the angle is one half of the arc it encompasses. So m∠S = 0.5 * arc PQR. Also m∠Q = 0.5 * arc PSR.
Think about this, arc PQS + arc RQS = 360°. We have a formula for each of these arc measurements in terms of x.
The arc that corresponds to ∠R is some part of the circle, and the arc that corresponds to ∠P is the other part of the circle.
(5x + 20) + (7x - 8) = 360
12x + 12 = 360
12x = 348
x = 29
if correct brainest! look at picture
Answer:
103.34 degrees
Step-by-step explanation:
The sum of angles in a triangle always equals 180 degrees. In other words, 40+(2x-30)+(x+20) = 180. Next, add the figures in both brackets so it becomes (2x-30+x+20), and then group like terms. (2x+x-30-20) which is 3x -50, because -30-20 is -50. The whole equation becomes 40+3x-50 = 180.
Group like terms again, so it becomes 30-50+3x = 180 which is -20+3x=180. Group like terms again but move the -20 to the side of the 180, and since it crosses the equal to sign, the - becomes + so it's 3x=180+20, resulting in 3x=200. Now to make x stand alone, we divide both sides by 3. 3x/3 is x and 200/3 is 66.6 recurring or 66.67. Now we know that x = 66.67, we substitute it in the formula for the angle at B. It becomes (2 times 66.67-30) which is 133.34 - 30, which becomes 103.34 as the answer. If told to round, it becomes 103 degrees.
hey I was wondering if somone could help me solve this problem -10/9=5w. The -10/9 is a fraction
Adrian started biking to the mall traveling 13 mph, after some time the bike got a flat so Adrian walked the rest of the way, traveling 3 mph. If the total trip to the mall took 9 hours and it was 87 miles away, how long did Adrian travel at each speed?
_____ hours at 3 mph
_____ hours at 13 mph
Answer:
Step-by-step explanation:
Let's denote the time that Adrian traveled on the bike at 13 mph by "t" and the time that he walked at 3 mph by "9 - t" (since the total trip took 9 hours).
Since we know that the total distance traveled was 87 miles, we can write the equation:
distance traveled on bike + distance traveled walking = 87
Using the formula distance = rate x time, we can express the distance traveled on the bike and walking in terms of time:
13t + 3(9 - t) = 87
Simplifying this equation:
13t + 27 - 3t = 87
10t = 60
t = 6
Therefore, Adrian traveled on the bike for 6 hours (at 13 mph) and walked for 3 hours (at 3 mph).
Type the correct answer in the box. Use numerals instead of words. What value of x satisfies this equation? log(2x)=2
The value of x that satisfies the equation log(2x) = 2 is 50, which is obtained by applying the definition of logarithms and simplifying the resulting equation.
The given equation is log(2x) = 2. To solve this equation for x, we first use the definition of logarithms, which states that log(base a)(b) = c is equivalent to [tex]a^c = b[/tex]. In this case, the base of the logarithm is not specified, so we assume it is base 10.
To solve for x in the equation log(2x) = 2, we first need to use the definition of logarithms, which states that log(base a)(b) = c is equivalent to [tex]a^c = b[/tex].
In this case, we have:
log(2x) = 2
Using the definition of logarithms, we can rewrite this as:
[tex]10^2 = 2x[/tex]
Simplifying, we get:
100 = 2x
Dividing both sides by 2, we get:
50 = x
Therefore, the value of x that satisfies the equation log(2x) = 2 is 50.
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